BLACKBODY
P = εσAT⁴ and λ_max = b/T — Stefan, Wien, and the Planck curve that broke classical physics.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Anything with a temperature glows. A person, a stove, a star — each pours out a whole spectrum of light set entirely by how hot it is. The two questions that opened the twentieth century: what colour does it glow, and how much power does it radiate?
Two laws
The spectrum is the Planck curve, and two simple laws capture its behaviour. Stefan–Boltzmann: the total power, the area under the curve, grows as temperature to the fourth power — a modest heating brings a fierce brightening. Wien: the peak wavelength shrinks as one over temperature, so hotter bodies glow bluer.
Solve
Multiply emissivity, the Stefan–Boltzmann constant, area, and T⁴ for total power; divide Wien’s constant by temperature for the spectral peak. A Sun-like peak near 502 nm does not make the Sun green: perceived color comes from integrating the entire visible spectrum, which the swatch now does.
Heating up
Watch the object heat from a dull ember toward its set temperature. The Planck curve swells — its area climbing as the fourth power — and its peak marches steadily leftward, crossing out of the infrared and into the visible. This is why a poker glows first red, then orange, then dazzling white as it gets hotter.
Audit
Audited: emissivity scales both the integrated power and plotted spectral height linearly without changing the shared graph scale; the Planck integral recovers εσT⁴; Wien locates the spectral peak; and the body swatch uses integrated blackbody chromaticity rather than the peak wavelength alone.